       Re: triangles in circles

• To: mathgroup at smc.vnet.net
• Subject: [mg26856] Re: [mg26813] triangles in circles
• From: Andrzej Kozlowski <andrzej at bekkoame.ne.jp>
• Date: Thu, 25 Jan 2001 01:13:32 -0500 (EST)
• Sender: owner-wri-mathgroup at wolfram.com

```Here is some quickly written code that will create the points on the circle
and the triangles you want. I make use of the Combinatorica package to
construct all the choices of three points out of n.

<< DiscreteMath`Combinatorica`

Next we get the coordinates of the points on the unit circle:

pts[n_] := {Re[#], Im[#]} & /@ Map[ExpToTrig, Table[E^(2Pi*I*k/n), {k, 1,
n}]]

Here are the triangles that can be made given n-points (n>2).

triangles[n_] :=
Line /@ KSubsets[pts[n], 3] /. Line[a_] :> Line[Append[a, First[a]]]

You can see them with:

Show[Graphics[{triangles}], AspectRatio -> Automatic]

This can be improved in various ways, by adding the ciorcle, colour etc.

--
Andrzej Kozlowski
Toyama International University
JAPAN

http://platon.c.u-tokyo.ac.jp/andrzej/
http://sigma.tuins.ac.jp/

on 1/24/01 6:18 PM, Tom De Vries at tdevries at shop.westworld.ca wrote:

> Hello all,
>
> I'm teaching a high school math class and we are doing permutations and
> combinations.  One of the "standard" questions is ..."given a certain number
> of points located around a circle, how many triangles can be formed...."
>
> The simple line below creates a circle with 5 points arranged around it.
> Could someone help me with a way to generate the lists of points that would
> create all the triangles.   I know that for more points it would get kind of
> messy, but I wanted to actually draw all the triangles as I thought it might
> be an interesting graphic...
>
>
>
> n = 5;
>
> ptlist = Table[{Cos[i 2 \[Pi]/n], Sin[i 2 \[Pi]/n]}, {i, 1, n}];
>
> Show[Graphics[{
> Circle[{0, 0}, 1],
> {PointSize[0.02], Point /@ ptlist}
> }], AspectRatio -> Automatic]
>
> Sincerely, Tom De Vries
>
>
>

```

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